A 'Nice' Bijection for a Content Formula for Skew Semistandard Young Tableaux

نویسنده

  • Martin Rubey
چکیده

Based on Schützenberger’s evacuation and a modification of jeu de taquin, we give a bijective proof of an identity connecting the generating function of reverse semistandard Young tableaux with bounded entries with the generating function of all semistandard Young tableaux. This solves Exercise 7.102 b of Richard Stanley’s book ‘Enumerative Combinatorics 2’.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Inversions of Semistandard Young Tableaux

A tableau inversion is a pair of entries from the same column of a row-standard tableau that lack the relative ordering necessary to make the tableau columnstandard. An i-inverted Young tableau is a row-standard tableau with precisely i inversion pairs, and may be interpreted as a generalization of (column-standard) Young tableaux. Inverted Young tableaux that lack repeated entries were introdu...

متن کامل

Jeu-de-taquin promotion and a cyclic sieving phenomenon for semistandard hook tableaux

Jeu-de-taquin promotion yields a bijection on the set of semistandard λ-tableaux with entries bounded by k. In this note, we determine the order of jeu-de-taquin promotion on the set of semistandard hook tableaux CST ((n−m, 1m), k), with entries bounded by k, and on the set of semistandard hook tableaux with fixed content α, CST ((n−m, 1m), k, α). We give a bijection between CST ((n−m, 1m), k, ...

متن کامل

An Explicit Bijection Between Semistandard Tableaux and Non-Elliptic sl3 Webs

The sl3 spider is a diagrammatic category used to study the representation theory of the quantum group Uq(sl3). The morphisms in this category are generated by a basis of non-elliptic webs. KhovanovKuperberg observed that non-elliptic webs are indexed by semistandard Young tableaux. They establish this bijection via a recursive growth algorithm. Recently, Tymoczko gave a simple version of this ...

متن کامل

Another Involution Principle-Free Bijective Proof of Stanley's Hook-Content Formula

Another bijective proof of Stanley’s hook-content formula for the generating function for semistandard tableaux of a given shape is given that does not involve the involution principle of Garsia and Milne. It is the result of a merge of the modified jeu de taquin idea from the author’s previous bijective proof (“An involution principle-free bijective proof of Stanley’s hook-content formula”, Di...

متن کامل

Sequences of Symmetric Polynomials and Combinatorial Properties of Tableaux

In 1977 G.P. Thomas has shown that the sequence of Schur polynomials associated to a partition can be comfortabely generated from the sequence of variables x = (x1; x2; x3; : : :) by the application of a mixed shift/multiplication operator, which in turn can be easily computed from the set SY T () of standard Young tableaux of shape. We generalise this construction, thereby making possible | fo...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Electr. J. Comb.

دوره 9  شماره 

صفحات  -

تاریخ انتشار 2002